Correction for “Scaling confirmation of the thermodynamic dislocation theory,” by J. S. Langer and K. C. Le, which was first published November 9, 2020; 10.1073/pnas.2018647117 (Proc. Natl. Acad. Sci. U.S.A. 117, 29431-29434). The authors note that the affiliation for K. C. Le should instead appear as two separate affiliations: Materials Mechanics Research Group, Ton Duc Thang University, Ho Chi Minh City 729000, Vietnam; and Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City 729000, Vietnam. The corrected author and affiliation lines appear below. The online version has been corrected.

The thermodynamic dislocation theory (TDT) is based on two highly unconventional assumptions: first, that driven systems containing large numbers of dislocations are subject to the second law of thermodynamics and second, that the controlling inverse timescale for these systems is the thermally activated rate at which entangled pairs of dislocations become unpinned from each other. Here, we show that these two assumptions predict a scaling relation for steady-state stress as a function of strain rate and that this relation is accurately obeyed over a wide range of experimental data for aluminum and copper. This scaling relation poses a stringent test for the validity of the TDT. The fact that the TDT passes this test means that a wide range of problems in solid mechanics, previously thought to be fundamentally intractable, can now be addressed with confidence.

The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of high-temperature deformation of aluminum and steel. Using physics-based parameters that we expect theoretically to be independent of strain rate and temperature, we are able to fit experimental stress-strain curves for three different strain rates and three different temperatures for each of these two materials. Our theoretical curves include yielding transitions at zero strain in agreement with experiment. We find that thermal softening effects are important even at the lowest temperatures and smallest strain rates.

The statistical-thermodynamic dislocation theory developed in our earlier studies is used here in an analysis of the experimental observations of adiabatic shear banding in steel by Marchand and Duffy (1988). Employing only a small set of physics-based parameters, we are able to explain experimental stress-strain curves, including yielding transitions and strain hardening, over wide ranges of temperatures and strain rates. We make a simple model of weak notch-like perturbations that, when driven hard enough, trigger shear banding instabilities that are quantitatively in agreement with those seen in the experiments.